Quantum mechanics postulates that physical states evolve in time via a linear unitary operator generated by a Hermitian Hamiltonian, ensuring the conservation of inner products and distinguishability between physically distinct states. This framework dictates that observables correspond to measurable outcomes (eigenvalues) of Hermitian operators, with transition probabilities determined by the squared magnitude of state overlaps according to Born's rule. The theory establishes a formal structure where classical equations of motion for expectation values emerge as limits derived from non-commuting operator algebra involving commutators rather than simple Poisson brackets.
Quantum mechanics postulates that physical states evolve in time via a linear unitary operator generated by a Hermitian Hamiltonian, ensuring the conservation of inner products and distinguishability…